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CHAPTER TWO
Celestial Mechanics
The Constellations
Do you remember the first night that you stood for the very first time under a clear night sky and
gazed with bewilderment at its beauty? And did you think something like this as you watched: ‘‘How
many stars there are! How can anyone make any sense of this mass of stars?’’
An attentive observer will soon notice that individual bright stars that are rather close together in
the sky seem to form simple geometric shapes – squares, rhombuses, crosses, circles, arches. Giving a
name to these shapes in the sky makes them more familiar to you and easier to locate again. That is
probably how the first constellations originated and obtained their names. We probably will never
know who the first person was to group stars into constellations, but it must have occurred a long time
ago, most likely when human beings started walking erect, looked up at the sky, and were bewildered
by its beauty.
By adding to the geometric shapes the dimmer stars the constellations changed from simple figures
into images of gods, heroes, animals, and everyday objects. All peoples of this world have projected
their beliefs onto the sky. Modern astronomers use the constellations from the ancient Greeks, which
include not only objects and animals in the sky but also ancient mythological heroes. That is why
various groups of constellations tell us stories about Greek myths and legends (Figure 2.2).
By the 1930s, there was sheer chaos in the sky. Apart from the classical constellations found on sky
charts, there were also all of those that had been marked in the sky throughout the long history of
astronomy. Especially in seventeenth and eighteenth centuries, astronomers almost competed with
each other to see who could invent more new constellations from the leftover stars (Figure 2.5).
By sailing the South Seas astronomers came to learn about stars that were not visible from Europe
or North Africa, and the need to introduce new constellations for the southern celestial hemisphere
B. Kambič, Viewing the Constellations with Binoculars, Patrick Moore’s Practical Astronomy Series,
DOI 10.1007/978-0-387-85355-0_2, Ó Springer ScienceþBusiness Media, LLC 2010
21
22
Viewing the Constellations with Binoculars
Figure 2.1 The winter
Orion is one of the richest
constellations in the sky.
Among its numerous
bright stars are the
seventh and ninth brightest stars in the sky – slivery-white Rigel and the
orange
Betelgeuse.
Apart from them there
are also some hidden
treasures in the constellation that are revealed by
even a small pair of binoculars – numerous nebulae and clusters – among
which the biggest attraction is surely the large
and bright Orion Nebula
Figure 2.2 The star
chart of Orion from the
wonderful Hevelli’s Uranography that was published in 1690
appeared. Native inhabitants already had numerous suggestions for these constellations, and some of
these were taken into account, while others were not.
Most of the constellations included only the brightest stars; nobody knew to which constellations
the fainter stars belonged. With the huge leaps in development of modern observational astronomy at
Celestial Mechanics
23
Figure 2.3 A modern
star chart of Orion with
the constellation borders
the beginning of the twentieth century, things began to change. In 1934, the International Astronomical Union divided the sky into 88 constellations with precisely defined borders. Today we know
exactly which constellation even the faintest star belongs to. For today’s astronomer, a constellation is
a specific part of the sky and not merely a few bright stars that form its shape (Figure 2.3).
A constellation is thus a limited part of the sky, with stars and all nonstellar objects that usually have
only one thing in common – they appear to be close together in our sky (and – as seen from Earth – seem
to be roughly in the same direction). In reality some stars can be relatively close, while the others can be
very far from each other and do not have any physical connection whatsoever. If we suddenly found
ourselves on a different planet several hundreds light years away from the Sun, the night sky would look
completely different to us.
Not all constellations are of the same size (Table 2.1), for in drawing the borders astronomers took
into account historical facts. The largest constellation in the sky is Hydra, while the smallest is the
famous Crux, which lies in the southern celestial hemisphere and was named in 1679.
Table 2.1 Alphabetic list of constellations
Latin name
Abbr.
Genitive
Meaning
Size [sq.8]
Page
Loc.
Andromeda
Antlia
Apus
Aquarius
Aquila
Ara
Aries
Auriga
Boötes
Caelum
Camelopardalis
Cancer
Canes Venatici
Canis Major
And
Ant
Aps
Aqr
Aql
Ara
Ari
Aur
Boo
Cae
Cam
Cnc
CVn
CMa
Andromedae
Antliae
Apodis
Aquarii
Aquilae
Arae
Arietis
Aurigae
Boötis
Caeli
Camelopardalis
Cancri
Canum Venaticorum
Canis Majoris
Andromeda
The Air Pump
The Bird of Paradise
The Water Carrier
The Eagle
The Altar
The Ram
The Charioteer
The Herdsman
The Chisel
The Giraffe
The Crab
The Hunting Dogs
The Great Dog
722
239
206
980
652
237
441
657
906
125
747
306
465
380
172
182
–
183
189
–
195
196
202
206
207
213
218
228
N
S
S
S
NS
S
N
N
N
S
N
N
N
S
24
Viewing the Constellations with Binoculars
Table 2.1 (continued)
Latin name
Abbr.
Genitive
Meaning
Size [sq.8]
Page
Loc.
Canis Minor
Capricornus
Carina
Cassiopeia
Centaurus
Cepheus
Cetus
Chamaeleon
Circinus
Columba
Coma Berenices
Corona Australis
Corona Borealis
Corvus
Crater
Crux
Cygnus
Delphinus
Dorado
Draco
Equuleus
Eridanus
Fornax
Gemini
Grus
Hercules
Horologium
Hydra
Hydrus
Indus
Lacerta
Leo
Leo Minor
Lepus
Libra
Lupus
Lynx
Lyra
Mensa
Microscopium
Monoceros
Musca
Norma
Octans
Ophiuchus
Orion
Pavo
Pegasus
Perseus
Phoenix
Pictor
Pisces
Piscis Austrinus
Puppis
CMi
Cap
Car
Cas
Cen
Cep
Cet
Cha
Cir
Col
Com
CrA
CrB
Crv
Crt
Cru
Cyg
Del
Dor
Dra
Equ
Eri
For
Gem
Gru
Her
Hor
Hya
Hyi
Ind
Lac
Leo
LMi
Lep
Lib
Lup
Lyn
Lyr
Men
Mic
Mon
Mus
Nor
Oct
Oph
Ori
Pav
Peg
Per
Phe
Pic
Psc
PsA
Pup
Canis Minoris
Capricorni
Carinae
Cassiopeiae
Centauri
Cephei
Ceti
Chamaeleontis
Circini
Columbae
Comae Berenices
Coronae Australis
Coronae Borealis
Corvi
Crateris
Crucis
Cygni
Delphini
Doradus
Draconis
Equulei
Eridani
Fornacis
Geminorum
Gruis
Herculis
Horologii
Hydrae
Hydri
Indi
Lacertae
Leonis
Leonis Minoris
Leporis
Librae
Lupi
Lyncis
Lyrae
Mensae
Microscopii
Monocerotis
Muscae
Normae
Octantis
Ophiuchi
Orionis
Pavonis
Pegasi
Persei
Phoenicis
Pictoris
Piscium
Piscis Austrini
Puppis
The Little Dog
The Sea Goat
The Keel
Cassiopeia
The Centaur
Cepheus
The Sea Monster
The Chameleon
The Compasses
The Dove
Berenice’s Hair
The Southern Crown
The Northern Crown
The Crow
The Cup
The Southern Cross
The Swan
The Dolphin
The Goldfish
The Dragon
The Foal
The River
The Furnace
The Twins
The Crane
Hercules
The Pendulum Clock
The Water Snake
The Little Water Snake
The Indian
The Lizard
The Lion
The Little Lion
The Hare
The Scales
The Wolf
The Lynx
The Lyre
The Table Mountain
The Microscope
The Unicorn
The Fly
The Set Square
The Octant
The Serpent Holder
The Hunter
The Peacock
The Winged Horse
The Victorious Hero
The Phoenix
The Painter’s Easel
The Fishes
The Southern Fish
The Stern
183
414
494
598
1060
588
1231
132
93
270
386
128
170
184
282
68
804
189
179
1083
72
1138
398
514
366
1225
249
1303
243
312
201
947
232
290
538
334
545
286
153
210
482
138
165
291
948
594
378
1121
615
469
247
889
245
673
233
234
–
236
243
247
252
–
–
260
261
268
269
271
271
–
272
287
–
288
287
294
296
297
395
301
206
307
–
–
314
316
325
326
330
332
334
335
–
342
343
–
332
–
352
364
–
376
382
438
–
391
395
397
N
S
S
N
S
N
NS
S
S
S
N
S
N
S
S
S
N
N
S
N
N
S
S
N
S
N
S
NS
S
S
N
N
N
S
S
S
N
N
S
S
NS
S
S
S
NS
NS
S
N
N
S
S
NS
S
S
Celestial Mechanics
25
Table 2.1 (continued)
Latin name
Abbr.
Genitive
Meaning
Size [sq.8]
Page
Loc.
Pyxis
Pyx
Pyxidis
The Compass
221
182
S
Reticulum
Ret
Reticuli
The Net
114
–
S
Sagitta
Sge
Sagittae
The Arrow
80
408
N
Sagittarius
Sgr
Sagittarii
The Archer
867
411
S
Scorpius
Sco
Scorpii
The Scorpion
497
428
S
Sculptor
Scl
Sculptoris
The Sculptor
475
438
S
Scutum
Sct
Scuti
The Shield
109
441
S
Serpens
Ser
Serpentis
The Serpent
636
444
NS
Serpens Caput
SCa
Serpentis Caput
The Serpent’s Head
428
444
NS
Serpens Cauda
SCd
Serpentis Cauda
The Serpent’s Tail
208
447
NS
Sextans
Sex
Sextantis
The Sextant
314
453
NS
Taurus
Tau
Tauri
The Bull
797
455
N
Telescopium
Tel
Telescopii
The Telescope
252
–
S
Triangulum
Tri
Trianguli
The Triangle
132
468
N
Triangulum Australe
TrA
Trianguli Australis
The Southern Triangle
110
–
S
Tucana
Tuc
Tucanae
The Toucan
295
–
S
Ursa Major
UMa
Ursae Majoris
The Great Bear
1280
473
N
Ursa Minor
UMi
Ursae Minoris
The Little Bear
256
482
N
Vela
Vel
Velorum
The Sails
500
485
S
Virgo
Vir
Virginis
The Virgin
1294
487
NS
Volans
Vol
Volantis
The Flying Fish
141
–
S
Vulpecula
Vul
Vulpeculae
The Fox
268
495
N
abbr. Genitive of the constellation’s name is used with names of the stars, double stars and variable stars: Alpha Orionis,
Delta Scuti . . . Many times it is abbreviated: instead of Alpha Orionis we write Alpha Ori, instead of Delta Scuti we write
Delta Sct . . .
size Size of the constellation in square degrees.
page Page in this book, where the constellation starts.
location If the constellation lies in the north celestial hemisphere (above the celestial equator) it is labeled as N; if it lies on
south celestial hemisphere, it is labeled as S. If the constellation lies along celestial equator, so that one part is on north
celestial hemisphere and the other is on south celestial hemisphere, it is labeled as NS.
Maybe some of you might be wondering why we can use the constellations from the ancient Greeks,
who lived roughly 2,500 years ago. Haven’t things changed since then? Today we know that everything
in the universe is moving. Our Solar System and all other stellar systems travel around the center of
our Galaxy, and every star also travels in its own direction at its own specific speed. However, great
distances divide us from the stars. It is true that a star may whizz across the universe with the fantastic
speed of 50 km/s, but if we observe this star, for instance, from 100 light years away (approximately 1
million billions kilometers), we will be able to recognize its movement only with the most precise
instruments. Centuries will pass before we will notice with our own eyes that a star has changed its
position in the sky. And for this example we have chosen a rather fast star that is relatively close to us.
Asterisms
The ancient astronomers often divided the constellations into smaller parts that were, in turn, given their
own names. We call such a part of a constellation that has its own name but does not have the importance
of a constellation an asterism. The best known asterisms that many wrongly consider to be constellations
are the Big and Little Dipper. In reality, the Big Dipper is a part of the constellation Ursa Major, while the
Little Dipper is part of the constellation Ursa Minor (Figure 2.4). Another well-known asterism is the
Hunter’s Belt, which is formed by three rather close and bright stars in the constellation of Orion.
26
Viewing the Constellations with Binoculars
Figure 2.4 The shape
of the Big Dipper
100,000 years ago,
today, and in another
100,000 years. The
appearance of constellations changes through
time; however, millennia
must pass for us to be
able to notice these
changes with the naked
eye
Figure 2.5 A part of a
star chart from 1835
(author Elijah H. Burritt),
in which we can see the
classic constellations as
well as Herchel’s telescope. It was created
from the dimmer stars
between Gemini, Lynx,
and Auriga by the Austrian astronomer Maximilian Hell at the end of the
eighteenth
century.
Today the constellation
no longer exists
The Celestial Sphere
When we look into a clear night sky it seems shaped like a ball, with Earth at its center. At any given
moment in time we can see half of the sphere from our observing point. The second half lies below the
horizon. The stars all appear equally distant from us and seem to be ‘‘pinned up’’ onto the inside of this
celestial sphere. However, this sphere does not remain motionless. If we memorize the position of a
certain bright star in relation to a nearby house or tree and then look at the same star from the same
point an hour or two later, we will notice that it has moved to the west. The sky rotates from the east to
the west (Figure 2.6). Of course, the rotation is not real; it just appears to be happening, for in reality
Earth is rotating around its axis and we are rotating with it.
Celestial Mechanics
27
Figure 2.6 Here’s how
you can tell that the sky is
really rotating. Place a
photographic camera on
a stable tripod and point
it toward the sky. If you
expose the image for a
long period of time, say,
for a couple of hours, arcs
of the stars will be shown
in the image, in this case
the northern part of the
sky. The star in the center
is Polaris
Every sphere that rotates around its axis has two points that do not change their position. These are
the poles, in our case represented by the north and south celestial poles. Because the rotation of the
sky is a consequence of Earth rotating around its axis, the celestial poles are exactly above Earth’s
geographic poles – the north celestial pole is directly above Earth’s North Pole and the south celestial
pole directly above the Earth’s South Pole.
In the same way as Earth the celestial sphere has its celestial equator, which lies directly above
Earth’s equator, or, to put it another way, exactly in the middle between the two poles. The celestial
equator is a great circle that divides the celestial sphere into two equal hemispheres: the Northern and
Southern Hemisphere.
Wherever we stand in Earth’s Northern Hemisphere to observe the sky, the north celestial pole and
celestial equator are always above the horizon, and the south celestial pole is always below the
horizon. Wherever we stand in Earth’s Southern Hemisphere to watch the sky, the north celestial
pole is always below the horizon, and the south celestial pole and celestial equator are always above
the horizon. If our observing point is exactly on the equator, the northern and southern celestial poles
are on the (mathematical) horizon, and the celestial equator is in the zenith (Figure 2.7).
Celestial Coordinates
Soon after people started observing and describing stars in the celestial sphere, the need for a
coordinate system arose. The system that was adopted made it simple to describe the position of
the star (or any other celestial body) using only two coordinates. This was possible because in general
stars do not change much in position relative to each other over time.
The celestial coordinate system is similar to the system we use for places on Earth. Geographic
latitude is represented in the sky by declination, while geographic longitude is represented by right
ascension. The choice of starting point for declination seemed to be obvious. It is measured in degrees
from the celestial equator to the north (+) or south (–) celestial pole. The declination of the stars on
the celestial equator is 08, on the north celestial pole +908, and on the south celestial pole –908. For
28
Viewing the Constellations with Binoculars
Figure 2.7 For all observers on Earth the sky appears to be a sphere with Earth (the observer) at the center. At any given
moment of time we can see one half of the sphere (if there are no high hills there); the other half lies below the horizon. In the
illustration we can see only the horizon for observer 1, that is, the observer watching from mid-northern geographic
latitudes. With a bit of imagination we can guess how observers on other parts of Earth can see the sky. Observer 3 is sitting
at the North Pole. In his zenith is the north celestial pole, and along his (mathematical) horizon runs the celestial equator.
Observer 4 is sitting at the South Pole. In his zenith lies the south celestial pole, and along his (mathematical) horizon also
runs the celestial equator. Observer 2 is sitting on the equator. In his zenith is the celestial equator, and on the horizon on
opposite sides lie the north and south celestial poles
more precise measurements of declination the degree is divided into 60 arcmin (0 ), and an arc minute
is divided into 60 arcsec (00 ) (Figure 2.8).
The selection of the coordinate starting point for the right ascension is – the same as on Earth – a
matter of choice. In the same way as all geographic meridians are equal among themselves (they are all
great circles on the sphere), so are the celestial meridians. Due to historic reasons we have agreed on
Earth that we will start counting geographic longitude from the meridian that runs through the
observatory in Greenwich, London. The coordinate starting point of the system on Earth is therefore
at the point at which the Greenwich meridian crosses the equator. At that point the geographic latitude
and longitude are both 08. In the same way, astronomers needed to select a point on the celestial equator
that would represent the starting point of the celestial coordinate system. They agreed that this would be
the point where the ecliptic crosses the celestial equator and in which the Sun is at the spring equinox.
This point is called the vernal point, or point g (gamma), and it lies in the constellation of Pisces.1
Right ascension is measured in hours, from 0 h to 24 h. Its starting point is the vernal point, and it grows
toward the east. The advantage of such a division (hours instead of degrees) lies in the fact that for every
1
The ecliptic is the apparent annual path of the Sun across the celestial sphere. In one year the Sun crosses the ecliptic
only once. The ecliptic is not parallel to the celestial equator but makes an angle of 238260 . The intersections are two
points. We have already mentioned the vernal point, and the second point is called the autumnal point, which is where
the sun is in the autumn equinox.
Celestial Mechanics
29
Figure 2.8 The sky
coordinate system can
best be understood if you
visualize the coordinate
system of latitudes and
meridians on Earth and
project it onto the sky.
Once again four observers are shown on Earth.
The first (1), who is observing the sky from midnorthern latitudes, can
see the complicated net
of the coordinate system
in the sky, depending of
the geographical direction of the sky he is looking toward (see Figures
on pages 32 and 33).
The remaining three
have better luck. Their
sky is extremely simple.
Detailed drawings of
what they see are shown
on figure 2.10
hour the sky rotates for approximately one right ascension hour. That is why it is simple to ascertain from
star charts when a certain constellation or star will be above the horizon. If, for instance, Orion is at its
highest above the horizon and we are interested when (in how many hours) we will be able to see Cancer, we
look at the central right ascension of the Orion (5.5 h) and the central right ascension of Cancer (8.5 h).
From this we can immediately see that Cancer will be at its highest in approximately 3 h. Looked at it this
way, the sky becomes a giant 24-h clock. But beware! On the equator the arc of 1 h measures 158, and the
closer we get to the poles, the coordinate system lines converge and the arcs, which represent 1 h, are
shorter and shorter (see illustration above).
A right ascension hour is divided into 60 minutes (min) and a minute is divided into 60 seconds (s).
The way you write minutes and seconds at the declination and right ascension is different, for they are
different. If 1 h of right ascension on the celestial equator equals an arc of 158, 1 min equals the arc of
150 , and 1 s the arc of 1500 .
Because the celestial sphere rotates, the coordinate system rotates with it. The position of the celestial
body on the celestial sphere can therefore always be given with two coordinates. To put it another way, if
we know the two coordinates, we can always find the celestial body on the celestial sphere.
Rotating Sky
At the beginning, we mentioned that the night sky rotates. In fact, it only appears to be rotating, for in
reality Earth is rotating around its axis. Because we know that Earth takes 24 h to make one complete
rotation, we would expect that the same star that is rising on the horizon at this moment will appear on
the horizon again in 24 h. However, observations show differently.
If we choose a bright star and note down the time this star sets behind the neighbor’s roof (or some
other clearly distinguishable and nonmoving object) we will discover that the next day (if viewed from
the same point), the star will set behind the roof 4 min earlier. This phenomenon is even more
30
Viewing the Constellations with Binoculars
Figure 2.9 Which stars will be circumpolar, which will rise and set, and which will never appear above horizon depends
on the geographic latitude of the observing point. If we move toward the equator, the north celestial pole moves toward the
horizon, and the area of the sky around the pole, where the stars never rise and set, becomes smaller. If we move towards the
north geographic pole, the north celestial pole moves toward the zenith, and the area of sky around the pole, where the stars
never rise and set, increases. What the sky looks like at its extreme points (exactly on the pole and on the equator) is shown in
the illustrations on the next page
noticeable if there is a longer period between the two observations. In other words, a star that is setting
behind the neighbor’s roof at the beginning of January at 10 p.m. will set behind the same roof at the
beginning of February at 8 p.m. and at the beginning of March as early as 6 p.m. Over the year the
constellations slowly drift toward the west, and on the east new ones appear. These changes in the sky
are a consequence of Earth revolving around the Sun. That is why in the spring there are different
constellations in the sky than in summer, autumn, or winter.
Imagine a celestial sphere with Polaris on it (or the position of the north celestial pole). We know
that the sky seems to rotate around Polaris. The stars that are close to the pole travel in smaller circles,
and those that are further travel in larger circles. Because Polaris lies at 458 above the horizon (when
viewed from mid-northern latitudes), the stars that are close to it are visible throughout the night and
throughout the year, for they rotate around the pole and never fall below the horizon. We call these
circumpolar stars. Stars that are far from the North Pole rise and set during their daily and annual
movements across the sky.
Of course, there are also stars that are close to the south celestial pole (from mid-northern latitudes
it is 458 below the horizon). These never come above our horizon during their daily and annual
movements (and can thus never be seen from mid-northern latitudes). Whether a star is considered
circumpolar or that it rises and sets or is never above the horizon depends on the geographical latitude
of the observing point and the declination of the star. On the north geographical pole, where we have
Polaris in the zenith and the celestial equator on the horizon, all stars above the celestial equator (with
a positive declination) are circumpolar stars, while those below the horizon (with a negative declination) can never be seen. On the south geographic pole the situation is exactly the opposite.
Celestial Mechanics
31
If our observing point is on Earth’s equator, we have the celestial equator in the zenith, while the poles
lie on the opposing sides of the horizon. In this case none of the stars is circumpolar, and throughout the
year we can see all stars (and constellations) that can be seen from Earth. (This is why large observatories
are built as close as possible to the equator.) If our observing point is somewhere in between, certain stars
always appear above the horizon, others rise and set, while some other can never be seen. Stars that rise
and set at a certain geographical latitude j have the declination d within the following limits:
ð90 jjjÞ5d5ð90 jjjÞ
Constantly above (below) the horizon is the star on a positive (negative) geographical latitude j, if its
declination d fulfils the condition:
constantly above on j > 0
constantly below on j < 0 d > (908– |j|)
Constantly below (above) the horizon is the star on the positive (negative) geographical latitude j, if
its declination d fulfils the condition:
constantly below on j > 0
constantly above on j < 0 d < (|j| –908)
For all of the above-stated conditions we have to take the absolute value for the negative (south)
geographical latitude.
On mid-northern latitudes, the circumpolar stars (constantly above the horizon) are around the
north celestial pole to the declination +458. These stars can be seen on any clear night throughout the
year. Constantly below the horizon (can never be seen) are stars with a declination below –458. Stars
with a declination of between +458 and –458 rise and set and can be seen only at certain periods of the
year (Figure 2.10).
Figure 2.10 The appearance of the sky for the observer on the north geographic pole (illustration left) and on the equator.
For an observer sitting on the north geographic pole, the stars rotate around the vertical axis and therefore never set during
the night or during the year. However, this observer can see only stars in the northern celestial hemisphere (those with a
positive declination), and he can never see those in the southern hemisphere. Sitting on Earth’s South Pole, the observer can
see the movement of stars just like the observer on the North Pole, except that he has the south celestial pole in his zenith and
can see all the stars in the southern celestial hemisphere (with a negative declination). However, he can’t see the ones in the
northern celestial hemisphere. The observer on the equator is in the best position. During the night and throughout the year
he can see all of the stars that can be seen from Earth
32
Viewing the Constellations with Binoculars
The Directions of the Sky and Using Star
Charts
W
N
Where is north, south, east, and west in the spherical sky? It is defined by the celestial coordinate
system. North is always in the direction of Polaris, regardless of which direction the binoculars are
pointing and how they are turned. Let’s look at the example.
All charts (in Part II of this book) are oriented so that north is up, east is on the left, south is down,
and west is on the right. In our search, for example, of the globular cluster M 13 in Hercules we can use
the chart on page 304, and if the constellation at the moment is above the eastern horizon, we have to
know the orientation of the coordinate system in this part of the sky. If the sought-after cluster is on
the chart above the Zeta, you will search for it in the sky in vain in that place. You have to turn the
chart approximately 458 counterclockwise, as seen in the figure below. The cluster is thus left of Zeta.
What about the other parts of the sky?
The coordinate sky net in various directions in places with median geographic latitude 458 has been
shown on schematic figures. When we are turned toward the south (see Figure 2 on next page), you do
not need to turn the charts at all. North truly is upward, south is downward, east is on the left, and west
is on your right. For the other parts of the sky, the position of the coordinate system is more complex,
as seen in Figures 1, 3, and 4.
S
E
Field of
View of
Binoculars
Figure 1 – View East
If we observe the stars above the eastern horizon, we have to rotate the chart for about 458 counterclockwise. If we are observing stars above the western horizon, we have to rotate the charts for about 458
clockwise. Only when the charts are turned in the right direction can we say that the sought-after object
is, for instance, above the selected star or below it or left or right of it. This is why we try to avoid such
descriptions, and instead describe the position of the celestial bodies as east of. . ., northwest of. . ., etc.
If we are observing the stars in a northerly direction, it depends on the position of the observed
body in which direction and to how many degrees we have to rotate the chart so it will show what we
can see in the sky. Experienced observers, who are well acquainted with the constellations, look at
the position and orientation of a constellation in that part of the sky they are observing and then
rotate the chart so that the orientation in the sky matches the chart. You do always need to know
where the north celestial pole or Polaris is, for this tells us which way is north, and then the other
Celestial Mechanics
33
N
E
Field of
View of W
Binoculars
S
Figure 2 – View South
N
E
Field of
View of
Binoculars
W
S
Figure 3 — View West
N
W
E
Field of
View of W
Binoculars
S
Figure 4 — View North
E
N
S
N
Field of
View of
Binoculars
S
W
E
Field of
View of
Binoculars
34
Viewing the Constellations with Binoculars
directions in the sky are easy to figure out. Let us here also point out that this seemingly complicated
orientation of the field of view becomes easier the more experienced in observation you become. An
experienced observer always knows how the field of view in the binoculars is oriented, without
needing to think about it.
Seasonal Charts
In the seasonal charts that follow numbered 1 (January) to 12 (December), we can see how the
constellations in the mid-northern latitudes change during the year. Every chart covers a piece of the
sky along the meridian2 from the southeast to the southwest (908) and from the northern to the
southern horizon. The charts depict the sky as it appears around midnight of the 15th of each month.
The times that they can be seen hold true for the local time zone. Various conditions (daylight saving
time, etc.) are not taken into account. This means that we have to add an hour to the times next to the
dates in which daylight saving time applies. The circle with the stretched out hand next to each chart
represents approximately 258 and is intended to be the rough estimation of the size of the individual
constellation. The charts represent a good aid to the beginner in his or her first encounters with
constellations. More on this in the First Steps section later.
2
A meridian is an imaginary great circle on the celestial sphere. It passes through the northern point on the horizon,
through the celestial pole, up to the zenith, through the southern point on the horizon, and through the nadir, and is
perpendicular to the local horizon.
Celestial Mechanics
35
Mid January Around Midnight
NorthEast
North
CrB
NorthWest
Cyg
Her
Peg
Lac
DRACO
CEPHEUS
Boo
URSA MINOR
CASSIOPEIA
North
Celestial
Pole
And
CVn
CAMELOPARDALIS
PERSEUS
URSA MAJOR
LMi
Zenith for
Mid-Northern
Latitudes
LYNX
AURIGA
25°
LEO
GEMINI
TAURUS
CANCER
CANIS
MINOR
ORION
This constellations are
seen on meridian also:
HYDRA
MONOCEROS
Sex
Eri
in mid February
around 10 p.m.;
CANIS
MAJOR
in mid March
around 8 p.m.;
in mid December
around 2 a.m.;
in mid November
around 4 a.m.
Pyx
SouthEast
Ant
PUPPIS
Lep
Col
South
SouthWest
36
Viewing the Constellations with Binoculars
Mid February Around Midnight
NorthEast
Cyg
North
LYRA
NorthWest
Lac
Psc
ANDROMEDA
CEPHEUS
Her
CASSIOPEIA
DRACO
PERSEUS
URSA MINOR
North
Celestial
Pole
Cam
Boo
AURIGA
URSA MAJOR
CVn
LYNX
Zenith for
Mid-Northern
Latitudes
LEO MINOR
GEMINI
25°
CANCER
LEO
CANIS
MINOR
VIRGO
ORION
HYDRA
This constellations are
seen on meridian also:
Mon
SEXTANS
in mid March
around 10 p.m.;
Crt
in mid January
around 2 a.m.;
CANIS
MAJOR
Crv
in mid December
around 4 a.m.;
PYXIS
ANTLIA
Pup
South
SouthEast
VELA
SouthWest
in mid November
around 6 a.m.
Celestial Mechanics
37
Mid March Around Midnight
NorthEast
Lac
And
North
NorthWest
Tri
CYGNUS
CASSIOPEIA
PERSEUS
CEPHEUS
Cam
North
Celestial
Pole
DRACO
AURIGA
URSA
MINOR
Her
Lyn
GEMINI
URSA MAJOR
Zenith for
Mid-Northern
Latitudes
BOÖTES
CANES
VENATICI
LEO MINOR
CANCER
25°
COMA
BERENICES
LEO
This constellations are
seen on meridian also:
VIRGO
HYDRA
SEXTANS
in mid April
around 10 p.m.;
CRATER
in mid February
around 2 a.m.;
CORVUS
in mid January
around 4 a.m.;
HYDRA
Ant
in mid December
around 6 a.m.
South
SouthEast
Cen
Pyx
SouthWest
38
Viewing the Constellations with Binoculars
Mid April Around Midnight
NorthEast
NorthWest
North
PERSEUS
Lac
AURIGA
CASSIOPEIA
Cam
CEPHEUS
CYGNUS
North
Celestial
Pole
URSA
MINOR
Lyn
DRACO
LYRA
URSA
MAJOR
HERCULES
LMi
CORONA
BOREALIS
Zenith for
Mid-Northern
Latitudes
CANES
VENATICI
BOÖTES
25°
COMA
BERENICES
LEO
SERPENS
CAPUT
VIRGO
This constellations are
seen on meridian also:
OPHIUCHUS
Sex
in mid May
around 10 p.m.;
Crt
Lib
Crv
in mid March
around 2 a.m.;
HYDRA
in mid February
around 4 a.m.;
SCORPIUS
SouthEast
LUPUS
CENTAURUS
South
SouthWest
in mid January
around 6 a.m.
Celestial Mechanics
39
Mid May Around Midnight
NorthEast
North
ANDROMEDA
NorthWest
AURIGA
PERSEUS
GEMINI
Cam
CASSIOPEIA
Lyn
Lac
CEPHEUS
North
Celestial
Pole
URSA
MINOR
URSA
MAJOR
CYGNUS
DRACO
LYRA
Zenith for
Mid-Northern
Latitudes
HERCULES
CORONA
BOREALIS
25°
CVn
Com
BOÖTES
SERPENS
CAPUT
VIRGO
SERPENS
CAUDA
This constellations are
seen on meridian also:
OPHIUCHUS
Aql
Sct
in mid June
around 10 p.m.;
LIBRA
in mid April
around 2 a.m.;
Crv
in mid March
around 4 a.m.;
in mid February
around 6 a.m.
SCORPIUS
HYDRA
SAGITTARIUS
LUPUS
SouthEast
South
Cen
SouthWest
40
Viewing the Constellations with Binoculars
Mid June Around Midnight
NorthEast
PERSEUS
NorthWest
Cnc
AURIGA
North
Tri
Lyn
Cam
ANDROMEDA
URSA
MAJOR
CASSIOPEIA
North
Celestial
Pole
URSA
MINOR
CEPHEUS
Lac
CVn
DRACO
Zenith for
Mid-Northern
Latitudes
CYGNUS
LYRA
CORONA
BOREALIS
HERCULES
BOÖTES
25°
Vul
Del
Sge
SERPENS
CAPUT
Equ
AQUILA
SERPENS
CAUDA
OPHIUCHUS
This constellations are
seen on meridian also:
SCUTUM
SAGITTARIUS
in mid July
around 10 p.m.;
Lib
SCORPIUS
Cap
Hya
SouthEast
CrA
South
Lup
SouthWest
in mid May
around 2 a.m.;
in mid April
around 4 a.m.
Celestial Mechanics
41
Mid July Around Midnight
NorthEast
NorthWest
Lyn
North
AURIGA
LMi
URSA MAJOR
PERSEUS
Cam
CVn
And
CASSIOPEIA
North
Celestial
Pole
URSA MINOR
Boo
CEPHEUS
DRACO
Lac
Peg
Zenith for
Mid-Northern
Latitudes
HERCULES
CYGNUS
LYRA
25°
VULPECULA
DELPHINUS
Peg
SAGITTA
SCa
EQUULEUS
Psc
AQUILA
SERPENS
CAUDA
OPHIUCHUS
AQUARIUS
This constellations are
seen on meridian also:
SCUTUM
in mid August
around 10 p.m.;
in mid June
around 2 a.m.;
in mid May
around 4 a.m.
SAGITTARIUS
CAPRICORNUS
PsA
Mic
SouthEast
South
CrA
Sco
SouthWest
42
Viewing the Constellations with Binoculars
Mid August Around Midnight
NorthEast
NorthWest
North
Lyn
Com
URSA MAJOR
CVn
AURIGA
BOÖTES
Cam
North
Celestial
Pole
URSA MINOR
PERSEUS
DRACO
CASSIOPEIA
Her
ANDROMEDA
CEPHEUS
LACERTA
Pcs
Zenith for
Mid-Northern
Latitudes
LYRA
CYGNUS
25°
VULPECULA
PEGASUS
SAGITTA
DELPHINUS
EQUULEUS
PISCES
AQUILA
SERPENS
CAUDA
This constellations are
seen on meridian also:
AQUARIUS
SCUTUM
in mid September
around 10 p.m.;
CAPRICORNUS
in mid October
around 8 p.m.;
Cet
PISCIS
AUSTRINUS
in mid November
around 6 p.m.;
SAGITTARIUS
SouthEast
Scl
GRUS
South
MICROSCOPIUM
SouthWest
in mid July
around 2 a.m.
Celestial Mechanics
43
NorthEast
Mid September Around Midnight
North
Cnc
BOÖTES
NorthWest
URSA MAJOR
Gem
Lyn
URSA
MINOR
Her
North
Celestial
Pole
AURIGA
DRACO
Cam
CEPHEUS
PERSEUS
CASSIOPEIA
CYGNUS
Zenith for
Mid-Northern
Latitudes
LACERTA
TRIANGULUM
ANDROMEDA
25°
Ari
PISCES
Del
PEGASUS
Equ
PISCES
AQUILA
This constellations are
seen on meridian also:
CETUS
AQUARIUS
in mid October
around 10 p.m.;
in mid November
around 8 p.m.;
in mid December
around 6 p.m.;
in mid August
around 2 a.m.
Cap
Eri
PsA
SCULPTOR
SouthEast
South
GRUS
SouthWest
44
Viewing the Constellations with Binoculars
Mid October Around Midnight
NorthEast
North
NorthWest
LMi
Her
URSA
MAJOR
DRACO
LYRA
URSA
MINOR
Lyn
North
Celestial
Pole
CYGNUS
CEPHEUS
CAMELOPARDALIS
AURIGA
CASSIOPEIA
Lac
Zenith for
Mid-Northern
Latitudes
PERSEUS
TRIANGULUM
ANDROMEDA
PEGASUS
TAURUS
ARIES
25°
PISCES
PISCES
CETUS
AQUARIUS
This constellations are
seen on meridian also:
in mid November
around 10 p.m.;
ERIDANUS
For
SouthEast
ERIDANUS
in mid December
around 8 p.m.;
South
Scl
PsA
SouthWest
in mid January
around 6 p.m.;
in mid September
around 2 a.m.
Celestial Mechanics
45
Mid November Around Midnight
NorthEast
NorthWest
Her
North
CVn
LYRA
DRACO
CYGNUS
URSA
MINOR
URSA MAJOR
North
Celestial
Pole
CEPHEUS
Lac
Lyn
CAMELOPARDALIS
CASSIOPEIA
PERSEUS
ANDROMEDA
Zenith for
Mid-Northern
Latitudes
AURIGA
TRIANGULUM
GEMINI
25°
PISCES
ARIES
TAURUS
PISCES
ORION
This constellations are
seen on meridian also:
Mon
CETUS
in mid December
around 10 p.m.;
ERIDANUS
in mid January
around 8 p.m.;
Lep
FORNAX
in mid October
around 2 a.m.;
in mid September
around 4 a.m.
CANIS
MAJOR
SouthEast
Col
Cae
South
ERIDANUS
Scl
SouthWest
46
Viewing the Constellations with Binoculars
Mid December Around Midnight
NorthEast
Her
Boo
North
NorthWest
CYGNUS
DRACO
CVn
URSA
MINOR
Lac
CEPHEUS
North
Celestial
Pole
CASSIOPEIA
URSA MAJOR
CAMELOPARDALIS
ANDROMEDA
Lyn
Zenith for
Mid-Northern
Latitudes
Tri
PERSEUS
AURIGA
Cnc
Ari
GEMINI
25°
TAURUS
Psc
MALI
PES
Hya
ORION
This constellations are
seen on meridian also:
Cet
MONOCEROS
ERIDANUS
in mid January
around 10 p.m.;
LEPUS
CANIS
MAJOR
in mid February
around 8 p.m.;
ERIDANUS
in mid November
around 2 a.m.;
For
COLUMBA
Pyx
SouthEast
Pup
South
CAELUM
SouthWest
in mid October
around 4 a.m.
Celestial Mechanics
47
Measuring Angles in the Sky
Astronomers measure the apparent distances between the stars in the sky with angles. (We say
‘‘apparent’’ because these are not the true distances between the stars.) Betelgeuse and Rigel in the
constellation of Orion are 18.58 apart. From Betelgeuse to Gemini it is 338. The apparent diameter
of the Moon and Sun is approximately 0.58. The comet tail is 908 long. The star is 158 above the
horizon.
15°
25
°
2°
For a rough orientation – especially as we take our first steps across the sky – we can utilize
something we always have on us, our hand. If we stretch it out and spread the fingers apart, we have
a protractor; with this we can estimate the angle distances in the sky.
First Steps
If you have a friend or an acquaintance who is already familiar with the constellations, it is best if he or
she helps you take your first steps across the sky and points out a few of the brightest stars and the
constellations associated with them. Once you are familiar with a few constellations, you can use the
seasonal charts (found in this book), a planisphere, a star atlas, or some other aids to find and
recognize the remaining constellations.
A lot of people are familiar with the asterism called the Big Dipper. If you are among them, you can
use the seasonal charts and first locate the neighboring constellations of the Great Bear and then their
neighboring constellations and so on across the sky. But if you do not know a single star and a single
constellation and want to learn how to recognize them by yourself using this book, then read the
following paragraph very carefully.
In general, recognizing what is in the sky is pretty simple. What you need to know to begin is the
rough direction of north–south from your observing point. You can define this direction with a
48
Viewing the Constellations with Binoculars
compass or by looking where the Sun is at midday – roughly south. At a certain date, say in mid-April
at midnight, when you are standing under a clear night sky and turn toward the south, the spring
constellations will cover the sky from the southern horizon across the zenith to the northern horizon.
The sky is dominated by three bright stars (see chart P1 on page 51): Arcturus in Boötes, Spica in
Virgo, and Regulus in Leo. It is enough to recognize one constellation, the one with the greatest
number of bright stars. From this starting point you can then simply find the neighboring constellations, then their neighboring constellations, and so on across the celestial sphere. But beware! When
you think you have found, for instance, Regulus and Leo, have a look at the chart that depicts stars up
to magnitude 5 (we will speak about stellar brightness and its unit magnitude in the next chapter),
which is found in the description of this constellation in the second part of this book (Figure 2.11A).
In addition to the brightest stars that make up the shape of constellation Leo, you also should try to
recognize all of the fainter stars. Only then can you be sure that you are truly looking at Leo. (It
happens all too often that beginning amateur astronomers search for too small patterns of stars and
are satisfied with the first grouping that is roughly similar to the one they are looking for.)
When you have established the location of Leo, you should look at seasonal chart 3 (a cutout from
this chart can be found on Figure 2.11B), which includes the constellation Leo, and notice that the
following constellations surround it: to the west is Cancer, north is Leo Minor, northeast is Coma
Berenices, southeast is Virgo, south is the Sextans, and southwest is the head of the Hydra. Once you
recognize these constellations, with the help of the descriptions that are included in the second part of
this book, you will already know seven constellations. And then you can travel ahead across the
celestial sphere.
Charts P1–P4 depict the spring, summer, autumn, and winter skies in the Northern Hemisphere,
with only the brightest stars and thus only the most visible constellations or asterisms. Alongside
the charts are the dates and hours of visibility. Novices in sky gazing should first – depending on the
season and time – find one of these constellations. This should be the starting point. For easier
Celestial Mechanics
49
Figure 2.11 Photography of Leo with stars up to magnitude 8
μ
54
δ
ε
ζ
γ
60
η
ϑ
β
52
ψ
46
M105
M66
α
M65
M96
ι
M95
R
Regulus
53
ρ
χ
ν
ο
31
π
Figure 2.11A Map of Leo with stars up to magnitude 5
orientation we have also drawn in some of the more important angle distances and an open,
stretched out hand, which represents approximately 258. The zenith is also a useful point for
orientation.
Places with no light pollution or smog are the most suitable for observing the night sky through
binoculars. But on a clear, moonless night there are so many stars in the sky that sometimes even the
more experienced observers can be mislead, let alone beginners. Thus, while you are still inside in a
bright room, take a good look at the brightest stars and the angles between them on the chart. Only
then should you step out under the night sky, turn toward the south, and for the first few minutes
50
Viewing the Constellations with Binoculars
CANES
VENATICI
LEO MINOR
CANCER
COMA
BERENICES
LEO
VIRGO
HYDRA
SEXTANS
CRATER
CORVUS
Figure 2.11B Leo and surrounding constellations
Figure 2.12 It helps to picture the charts for learning about constellations (P1 to P4, as well as the seasonal charts) folded
over the meridian of the observing point from the south across the zenith to the north. If you have a problem with this, you
should photocopy the chart from this book and then bend it while using it during observation
Celestial Mechanics
51
NorthWest
NorthEast
Geographical
Latitude
North
CASSIOPEIA
Polaris
North Celestial Pole
URSA
MINOR
Alpha and Betha
point towards
Polaris.
URSA MAJOR
Zenith for
Mid-Northern
Latitudes
25°
BOÖTES
Arcturus
~55°
LEO
Regulus
~32°
The appearance of the
sky near meridian at:
mid January at 6 a.m.,
end January at 5 a.m.,
mid February at 4 a.m.,
end February at 3 a.m.,
mid March at 2 a.m.,
end March at 1 a.m.,
mid April at midnight,
end April at 11 p.m.,
mid May at 10 p.m.,
end May at 9 p.m.
VIRGO
~50°
Spica
South
SouthEast
SouthWest
52
Viewing the Constellations with Binoculars
NorthWest
NorthEast
Geographical
Latitude
North
URSA
MAJOR
Polaris
North Celestial Pole
CASSIOPEIA
URSA MINOR
Deneb
Zenith for
Mid-Northern
Latitudes
CYGNUS
25°
Vega
LYRA
Summer
Triangle
Altair
AQUILA
South
SouthEast
The appearance of the sky
near meridian at:
end May at 4 a.m.,
begin June ob 3 a.m.,
end June at 2 a.m.,
begin July ob 1 v,
end July at midnight,
begin August ob 11 p.m.,
end August at 10 p.m.,
begin September ob 9 p.m.,
end September at 8 p.m.,
begin October ob 7 p.m.,
South- end October at 6 p.m.
West
Celestial Mechanics
53
NorthWest
Geographical Latitude
NorthEast
North
URSA MAJOR
URSA
MINOR
Polaris
North Celestial Pole
CASSIOPEIA
Zenith for
Mid-Northern
Latitudes
25°
The Great Square
of Pegasus
(~15°x15°)
The appearance of the sky
near meridian at:
begin August at 3 a.m.,
mid August at 2 a.m.,
end August at 1 a.m.,
mid September at midnight,
end September at 11 p.m.,
mid October at 10 p.m.,
end October at 9 p.m.,
mid November at 8 p.m.,
end November at 7 p.m.,
mid December at 6 p.m. South-
East
PEGASUS
South
SouthWest
54
Viewing the Constellations with Binoculars
NorthWest
NorthEast
URSA MINOR
North
Celestial
Pole
Geographical
Latitude
North
Polaris
CASSIOPEIA
URSA MAJOR
Zenith for
Mid-Northern
Latitudes
~44°
Pollux
Capella
25°
AURIGA
~31°
GEMINI
~23°
TAURUS
Aldebaran
Betelgeuse
CANIS
MINOR
Procyon
~26°
Winter
Hexagon
ORION
~25°
Rigel
~22°
Sirius
CANIS
MAJOR
South
SouthEast
The appearance of the sky
near meridian at:
mid September at 6 a.m.,
end September at 5 a.m.,
mid October at 4 a.m.,
end October at 3 a.m.,
mid November at 2 a.m.,
end November at 1 a.m.,
mid December at midnight,
end December at 11 p.m.,
mid January at 10 p.m.,
end January at 9 p.m.,
mid February at 8 p.m.,
begin March at 7 p.m.,
Southmid March at 6 p.m.
West
Celestial Mechanics
55
while your eyes are still getting adjusted to the dark, you will see only the brightest stars and will
certainly recognize them.
You can also bring a flashlight outside with you. When you turn it off, your eyes will not have had
time to adjust to the dark, and you will only see the brightest stars in the sky. You can also try and
learn about the constellations by observing them from light polluted places, where even under the best
conditions you will only see stars up to magnitude 3, which, for the novice, is almost ideal. However,
after you are able to recognize the brightest stars and want to learn about the entire constellation, you
should find an observing point with dark, clear skies.
A final possibility is to start learning about the constellations at twilight, when the Sun has already
set but it is not yet night, and only the brightest stars are visible in the sky. Such conditions exist every
day for approximately half an hour.
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